TSTP Solution File: SEU395+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:06:52 EDT 2023
% Result : Theorem 7.70s 1.69s
% Output : CNFRefutation 7.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 139 ( 26 unt; 0 def)
% Number of atoms : 807 ( 11 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 1075 ( 407 ~; 473 |; 166 &)
% ( 5 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 200 ( 0 sgn; 101 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
fof(f34,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow19) ).
fof(f40,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f63,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_pre_topc) ).
fof(f73,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_yellow19) ).
fof(f76,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow19) ).
fof(f125,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_yellow19) ).
fof(f126,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow19) ).
fof(f127,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<=> is_a_convergence_point_of_set(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow19) ).
fof(f128,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<=> is_a_convergence_point_of_set(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[],[f127]) ).
fof(f133,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f247,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f248,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f247]) ).
fof(f249,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f253,plain,
! [X0,X1,X2] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f252]) ).
fof(f255,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f270,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f271,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f270]) ).
fof(f287,plain,
! [X0,X1,X2] :
( ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f288,plain,
! [X0,X1,X2] :
( ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f287]) ).
fof(f293,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f294,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f293]) ).
fof(f339,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f125]) ).
fof(f340,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f339]) ).
fof(f341,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f126]) ).
fof(f342,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f341]) ).
fof(f343,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<~> is_a_convergence_point_of_set(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f344,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<~> is_a_convergence_point_of_set(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f343]) ).
fof(f350,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f133]) ).
fof(f351,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f350]) ).
fof(f453,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,lim_points_of_net(X0,X1))
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
& ( is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f340]) ).
fof(f454,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f344]) ).
fof(f455,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f454]) ).
fof(f456,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK46,X1,X2)
| ~ in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),X1))) )
& ( is_a_convergence_point_of_set(sK46,X1,X2)
| in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),X1))) )
& element(X2,the_carrier(sK46)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK46)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK46)))
& ~ empty(X1) )
& top_str(sK46)
& topological_space(sK46)
& ~ empty_carrier(sK46) ) ),
introduced(choice_axiom,[]) ).
fof(f457,plain,
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK46,X1,X2)
| ~ in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),X1))) )
& ( is_a_convergence_point_of_set(sK46,X1,X2)
| in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),X1))) )
& element(X2,the_carrier(sK46)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK46)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK46)))
& ~ empty(X1) )
=> ( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK46,sK47,X2)
| ~ in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& ( is_a_convergence_point_of_set(sK46,sK47,X2)
| in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& element(X2,the_carrier(sK46)) )
& element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& proper_element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
& filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
& ~ empty(sK47) ) ),
introduced(choice_axiom,[]) ).
fof(f458,plain,
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK46,sK47,X2)
| ~ in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& ( is_a_convergence_point_of_set(sK46,sK47,X2)
| in(X2,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& element(X2,the_carrier(sK46)) )
=> ( ( ~ is_a_convergence_point_of_set(sK46,sK47,sK48)
| ~ in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& ( is_a_convergence_point_of_set(sK46,sK47,sK48)
| in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& element(sK48,the_carrier(sK46)) ) ),
introduced(choice_axiom,[]) ).
fof(f459,plain,
( ( ~ is_a_convergence_point_of_set(sK46,sK47,sK48)
| ~ in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& ( is_a_convergence_point_of_set(sK46,sK47,sK48)
| in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) )
& element(sK48,the_carrier(sK46))
& element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& proper_element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
& upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
& filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
& ~ empty(sK47)
& top_str(sK46)
& topological_space(sK46)
& ~ empty_carrier(sK46) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48])],[f455,f458,f457,f456]) ).
fof(f533,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f534,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f538,plain,
! [X2,X0,X1] :
( net_str(net_of_bool_filter(X0,X1,X2),X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f253]) ).
fof(f542,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f578,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f607,plain,
! [X2,X0,X1] :
( ~ empty_carrier(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f609,plain,
! [X2,X0,X1] :
( transitive_relstr(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f618,plain,
! [X2,X0,X1] :
( directed_relstr(net_of_bool_filter(X0,X1,X2))
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f821,plain,
! [X2,X0,X1] :
( is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f453]) ).
fof(f822,plain,
! [X2,X0,X1] :
( in(X2,lim_points_of_net(X0,X1))
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f453]) ).
fof(f823,plain,
! [X0,X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f824,plain,
~ empty_carrier(sK46),
inference(cnf_transformation,[],[f459]) ).
fof(f825,plain,
topological_space(sK46),
inference(cnf_transformation,[],[f459]) ).
fof(f826,plain,
top_str(sK46),
inference(cnf_transformation,[],[f459]) ).
fof(f827,plain,
~ empty(sK47),
inference(cnf_transformation,[],[f459]) ).
fof(f828,plain,
filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46))),
inference(cnf_transformation,[],[f459]) ).
fof(f829,plain,
upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46))),
inference(cnf_transformation,[],[f459]) ).
fof(f830,plain,
proper_element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46))))),
inference(cnf_transformation,[],[f459]) ).
fof(f831,plain,
element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46))))),
inference(cnf_transformation,[],[f459]) ).
fof(f832,plain,
element(sK48,the_carrier(sK46)),
inference(cnf_transformation,[],[f459]) ).
fof(f833,plain,
( is_a_convergence_point_of_set(sK46,sK47,sK48)
| in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) ),
inference(cnf_transformation,[],[f459]) ).
fof(f834,plain,
( ~ is_a_convergence_point_of_set(sK46,sK47,sK48)
| ~ in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) ),
inference(cnf_transformation,[],[f459]) ).
fof(f840,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f351]) ).
cnf(c_97,plain,
( ~ net_str(X0,X1)
| ~ transitive_relstr(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ directed_relstr(X0)
| element(lim_points_of_net(X1,X0),powerset(the_carrier(X1)))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f533]) ).
cnf(c_98,plain,
( ~ one_sorted_str(X0)
| element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f534]) ).
cnf(c_100,plain,
( ~ element(X0,powerset(the_carrier(boole_POSet(X1))))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ upper_relstr_subset(X0,boole_POSet(X1))
| ~ filtered_subset(X0,boole_POSet(X1))
| ~ one_sorted_str(X2)
| net_str(net_of_bool_filter(X2,X1,X0),X2)
| empty_carrier(X2)
| empty(X0)
| empty(X1) ),
inference(cnf_transformation,[],[f538]) ).
cnf(c_106,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f542]) ).
cnf(c_142,plain,
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f578]) ).
cnf(c_172,plain,
( ~ element(X0,powerset(the_carrier(boole_POSet(X1))))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ upper_relstr_subset(X0,boole_POSet(X1))
| ~ filtered_subset(X0,boole_POSet(X1))
| ~ one_sorted_str(X2)
| transitive_relstr(net_of_bool_filter(X2,X1,X0))
| empty_carrier(X2)
| empty(X0)
| empty(X1) ),
inference(cnf_transformation,[],[f609]) ).
cnf(c_174,plain,
( ~ element(X0,powerset(the_carrier(boole_POSet(X1))))
| ~ empty_carrier(net_of_bool_filter(X2,X1,X0))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ upper_relstr_subset(X0,boole_POSet(X1))
| ~ filtered_subset(X0,boole_POSet(X1))
| ~ one_sorted_str(X2)
| empty_carrier(X2)
| empty(X0)
| empty(X1) ),
inference(cnf_transformation,[],[f607]) ).
cnf(c_178,plain,
( ~ element(X0,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X0,powerset(the_carrier(boole_POSet(X1))))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ upper_relstr_subset(X0,boole_POSet(X1))
| ~ filtered_subset(X0,boole_POSet(X1))
| ~ one_sorted_str(X2)
| directed_relstr(net_of_bool_filter(X2,X1,X0))
| empty_carrier(X2)
| empty(X0)
| empty(X1) ),
inference(cnf_transformation,[],[f618]) ).
cnf(c_385,plain,
( ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ directed_relstr(X1)
| in(X2,lim_points_of_net(X0,X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f822]) ).
cnf(c_386,plain,
( ~ in(X0,lim_points_of_net(X1,X2))
| ~ element(X0,the_carrier(X1))
| ~ net_str(X2,X1)
| ~ transitive_relstr(X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ directed_relstr(X2)
| is_a_convergence_point_of_set(X1,filter_of_net_str(X1,X2),X0)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f821]) ).
cnf(c_387,plain,
( ~ element(X0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
| ~ proper_element(X0,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X1)))))
| ~ upper_relstr_subset(X0,boole_POSet(cast_as_carrier_subset(X1)))
| ~ filtered_subset(X0,boole_POSet(cast_as_carrier_subset(X1)))
| ~ one_sorted_str(X1)
| filter_of_net_str(X1,net_of_bool_filter(X1,cast_as_carrier_subset(X1),X0)) = X0
| empty_carrier(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f823]) ).
cnf(c_388,negated_conjecture,
( ~ in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)))
| ~ is_a_convergence_point_of_set(sK46,sK47,sK48) ),
inference(cnf_transformation,[],[f834]) ).
cnf(c_389,negated_conjecture,
( in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)))
| is_a_convergence_point_of_set(sK46,sK47,sK48) ),
inference(cnf_transformation,[],[f833]) ).
cnf(c_390,negated_conjecture,
element(sK48,the_carrier(sK46)),
inference(cnf_transformation,[],[f832]) ).
cnf(c_391,negated_conjecture,
element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46))))),
inference(cnf_transformation,[],[f831]) ).
cnf(c_392,negated_conjecture,
proper_element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46))))),
inference(cnf_transformation,[],[f830]) ).
cnf(c_393,negated_conjecture,
upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46))),
inference(cnf_transformation,[],[f829]) ).
cnf(c_394,negated_conjecture,
filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46))),
inference(cnf_transformation,[],[f828]) ).
cnf(c_395,negated_conjecture,
~ empty(sK47),
inference(cnf_transformation,[],[f827]) ).
cnf(c_396,negated_conjecture,
top_str(sK46),
inference(cnf_transformation,[],[f826]) ).
cnf(c_397,negated_conjecture,
topological_space(sK46),
inference(cnf_transformation,[],[f825]) ).
cnf(c_398,negated_conjecture,
~ empty_carrier(sK46),
inference(cnf_transformation,[],[f824]) ).
cnf(c_404,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f840]) ).
cnf(c_434,plain,
( ~ top_str(sK46)
| one_sorted_str(sK46) ),
inference(instantiation,[status(thm)],[c_106]) ).
cnf(c_491,plain,
( ~ empty(cast_as_carrier_subset(sK46))
| ~ one_sorted_str(sK46)
| empty_carrier(sK46) ),
inference(instantiation,[status(thm)],[c_142]) ).
cnf(c_495,plain,
( ~ one_sorted_str(sK46)
| element(cast_as_carrier_subset(sK46),powerset(the_carrier(sK46))) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_713,plain,
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_106]) ).
cnf(c_714,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(renaming,[status(thm)],[c_713]) ).
cnf(c_5115,plain,
( X0 != sK46
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ directed_relstr(X1)
| in(X2,lim_points_of_net(X0,X1))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_385,c_397]) ).
cnf(c_5116,plain,
( ~ is_a_convergence_point_of_set(sK46,filter_of_net_str(sK46,X0),X1)
| ~ element(X1,the_carrier(sK46))
| ~ net_str(X0,sK46)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ top_str(sK46)
| in(X1,lim_points_of_net(sK46,X0))
| empty_carrier(X0)
| empty_carrier(sK46) ),
inference(unflattening,[status(thm)],[c_5115]) ).
cnf(c_5118,plain,
( empty_carrier(X0)
| in(X1,lim_points_of_net(sK46,X0))
| ~ is_a_convergence_point_of_set(sK46,filter_of_net_str(sK46,X0),X1)
| ~ element(X1,the_carrier(sK46))
| ~ net_str(X0,sK46)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5116,c_396,c_398,c_5116]) ).
cnf(c_5119,plain,
( ~ is_a_convergence_point_of_set(sK46,filter_of_net_str(sK46,X0),X1)
| ~ element(X1,the_carrier(sK46))
| ~ net_str(X0,sK46)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| in(X1,lim_points_of_net(sK46,X0))
| empty_carrier(X0) ),
inference(renaming,[status(thm)],[c_5118]) ).
cnf(c_5205,plain,
( X0 != sK46
| ~ in(X1,lim_points_of_net(X0,X2))
| ~ element(X1,the_carrier(X0))
| ~ net_str(X2,X0)
| ~ transitive_relstr(X2)
| ~ top_str(X0)
| ~ directed_relstr(X2)
| is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X2),X1)
| empty_carrier(X0)
| empty_carrier(X2) ),
inference(resolution_lifted,[status(thm)],[c_386,c_397]) ).
cnf(c_5206,plain,
( ~ in(X0,lim_points_of_net(sK46,X1))
| ~ element(X0,the_carrier(sK46))
| ~ net_str(X1,sK46)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ top_str(sK46)
| is_a_convergence_point_of_set(sK46,filter_of_net_str(sK46,X1),X0)
| empty_carrier(X1)
| empty_carrier(sK46) ),
inference(unflattening,[status(thm)],[c_5205]) ).
cnf(c_5208,plain,
( empty_carrier(X1)
| is_a_convergence_point_of_set(sK46,filter_of_net_str(sK46,X1),X0)
| ~ in(X0,lim_points_of_net(sK46,X1))
| ~ element(X0,the_carrier(sK46))
| ~ net_str(X1,sK46)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1) ),
inference(global_subsumption_just,[status(thm)],[c_5206,c_396,c_398,c_5206]) ).
cnf(c_5209,plain,
( ~ in(X0,lim_points_of_net(sK46,X1))
| ~ element(X0,the_carrier(sK46))
| ~ net_str(X1,sK46)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| is_a_convergence_point_of_set(sK46,filter_of_net_str(sK46,X1),X0)
| empty_carrier(X1) ),
inference(renaming,[status(thm)],[c_5208]) ).
cnf(c_5232,plain,
( X0 != sK46
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ top_str(X0)
| ~ directed_relstr(X1)
| element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_97,c_397]) ).
cnf(c_5233,plain,
( ~ net_str(X0,sK46)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ top_str(sK46)
| element(lim_points_of_net(sK46,X0),powerset(the_carrier(sK46)))
| empty_carrier(X0)
| empty_carrier(sK46) ),
inference(unflattening,[status(thm)],[c_5232]) ).
cnf(c_5235,plain,
( empty_carrier(X0)
| element(lim_points_of_net(sK46,X0),powerset(the_carrier(sK46)))
| ~ net_str(X0,sK46)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0) ),
inference(global_subsumption_just,[status(thm)],[c_5233,c_396,c_398,c_5233]) ).
cnf(c_5236,plain,
( ~ net_str(X0,sK46)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| element(lim_points_of_net(sK46,X0),powerset(the_carrier(sK46)))
| empty_carrier(X0) ),
inference(renaming,[status(thm)],[c_5235]) ).
cnf(c_5306,plain,
( X0 != sK46
| one_sorted_str(X0) ),
inference(resolution_lifted,[status(thm)],[c_714,c_396]) ).
cnf(c_5307,plain,
one_sorted_str(sK46),
inference(unflattening,[status(thm)],[c_5306]) ).
cnf(c_47634,plain,
( ~ in(X0,lim_points_of_net(sK46,X1))
| ~ net_str(X1,sK46)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| element(X0,the_carrier(sK46))
| empty_carrier(X1) ),
inference(superposition,[status(thm)],[c_5236,c_404]) ).
cnf(c_48158,plain,
( ~ in(X0,lim_points_of_net(sK46,X1))
| ~ net_str(X1,sK46)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| is_a_convergence_point_of_set(sK46,filter_of_net_str(sK46,X1),X0)
| empty_carrier(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5209,c_47634]) ).
cnf(c_49908,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ one_sorted_str(X0)
| transitive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0)
| empty(sK47) ),
inference(superposition,[status(thm)],[c_391,c_172]) ).
cnf(c_49912,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| transitive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49908,c_395,c_394,c_393]) ).
cnf(c_50410,plain,
( transitive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| empty_carrier(X0) ),
inference(global_subsumption_just,[status(thm)],[c_49912,c_396,c_398,c_434,c_491,c_49912]) ).
cnf(c_50411,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| transitive_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| empty_carrier(X0) ),
inference(renaming,[status(thm)],[c_50410]) ).
cnf(c_50421,plain,
( ~ one_sorted_str(sK46)
| transitive_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| empty_carrier(sK46) ),
inference(superposition,[status(thm)],[c_98,c_50411]) ).
cnf(c_50422,plain,
transitive_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)),
inference(forward_subsumption_resolution,[status(thm)],[c_50421,c_398,c_5307]) ).
cnf(c_50547,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ one_sorted_str(X0)
| net_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47),X0)
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0)
| empty(sK47) ),
inference(superposition,[status(thm)],[c_391,c_100]) ).
cnf(c_50552,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| net_str(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47),X0)
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50547,c_395,c_394,c_393]) ).
cnf(c_50710,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(sK46)))
| ~ one_sorted_str(sK46)
| net_str(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47),sK46)
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(sK46) ),
inference(instantiation,[status(thm)],[c_50552]) ).
cnf(c_51005,plain,
( ~ empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ one_sorted_str(X0)
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0)
| empty(sK47) ),
inference(superposition,[status(thm)],[c_391,c_174]) ).
cnf(c_51010,plain,
( ~ empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51005,c_395,c_394,c_393]) ).
cnf(c_51378,plain,
( ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| empty_carrier(X0) ),
inference(global_subsumption_just,[status(thm)],[c_51010,c_396,c_398,c_434,c_491,c_51010]) ).
cnf(c_51379,plain,
( ~ empty_carrier(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(renaming,[status(thm)],[c_51378]) ).
cnf(c_51389,plain,
( ~ empty_carrier(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| ~ one_sorted_str(sK46)
| empty_carrier(sK46) ),
inference(superposition,[status(thm)],[c_98,c_51379]) ).
cnf(c_51390,plain,
~ empty_carrier(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)),
inference(forward_subsumption_resolution,[status(thm)],[c_51389,c_398,c_5307]) ).
cnf(c_51512,plain,
( ~ proper_element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
| ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ one_sorted_str(X0)
| directed_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0)
| empty(sK47) ),
inference(superposition,[status(thm)],[c_391,c_178]) ).
cnf(c_51517,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| directed_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| empty(cast_as_carrier_subset(sK46))
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51512,c_395,c_394,c_393,c_392]) ).
cnf(c_51812,plain,
( directed_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| ~ one_sorted_str(X0)
| ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| empty_carrier(X0) ),
inference(global_subsumption_just,[status(thm)],[c_51517,c_396,c_398,c_434,c_491,c_51517]) ).
cnf(c_51813,plain,
( ~ element(cast_as_carrier_subset(sK46),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| directed_relstr(net_of_bool_filter(X0,cast_as_carrier_subset(sK46),sK47))
| empty_carrier(X0) ),
inference(renaming,[status(thm)],[c_51812]) ).
cnf(c_51823,plain,
( ~ one_sorted_str(sK46)
| directed_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| empty_carrier(sK46) ),
inference(superposition,[status(thm)],[c_98,c_51813]) ).
cnf(c_51824,plain,
directed_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)),
inference(forward_subsumption_resolution,[status(thm)],[c_51823,c_398,c_5307]) ).
cnf(c_51932,plain,
( ~ element(sK47,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK46)))))
| ~ upper_relstr_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ filtered_subset(sK47,boole_POSet(cast_as_carrier_subset(sK46)))
| ~ one_sorted_str(sK46)
| filter_of_net_str(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)) = sK47
| empty_carrier(sK46)
| empty(sK47) ),
inference(superposition,[status(thm)],[c_392,c_387]) ).
cnf(c_51933,plain,
filter_of_net_str(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)) = sK47,
inference(forward_subsumption_resolution,[status(thm)],[c_51932,c_395,c_398,c_5307,c_394,c_393,c_391]) ).
cnf(c_52106,plain,
( ~ in(X0,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)))
| ~ net_str(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47),sK46)
| ~ transitive_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| ~ directed_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| empty_carrier(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| is_a_convergence_point_of_set(sK46,sK47,X0) ),
inference(superposition,[status(thm)],[c_51933,c_48158]) ).
cnf(c_52107,plain,
( ~ net_str(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47),sK46)
| ~ transitive_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| ~ directed_relstr(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))
| ~ element(X0,the_carrier(sK46))
| ~ is_a_convergence_point_of_set(sK46,sK47,X0)
| in(X0,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)))
| empty_carrier(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)) ),
inference(superposition,[status(thm)],[c_51933,c_5119]) ).
cnf(c_52108,plain,
( ~ in(X0,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)))
| ~ net_str(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47),sK46)
| is_a_convergence_point_of_set(sK46,sK47,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52106,c_51390,c_51824,c_50422]) ).
cnf(c_52112,plain,
( ~ net_str(net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47),sK46)
| ~ element(X0,the_carrier(sK46))
| ~ is_a_convergence_point_of_set(sK46,sK47,X0)
| in(X0,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52107,c_51390,c_51824,c_50422]) ).
cnf(c_52189,plain,
( ~ in(X0,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47)))
| is_a_convergence_point_of_set(sK46,sK47,X0) ),
inference(global_subsumption_just,[status(thm)],[c_52108,c_396,c_398,c_434,c_491,c_495,c_50710,c_52108]) ).
cnf(c_52196,plain,
is_a_convergence_point_of_set(sK46,sK47,sK48),
inference(backward_subsumption_resolution,[status(thm)],[c_389,c_52189]) ).
cnf(c_52197,plain,
~ in(sK48,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))),
inference(backward_subsumption_resolution,[status(thm)],[c_388,c_52189]) ).
cnf(c_52352,plain,
( ~ element(X0,the_carrier(sK46))
| ~ is_a_convergence_point_of_set(sK46,sK47,X0)
| in(X0,lim_points_of_net(sK46,net_of_bool_filter(sK46,cast_as_carrier_subset(sK46),sK47))) ),
inference(global_subsumption_just,[status(thm)],[c_52112,c_396,c_398,c_434,c_491,c_495,c_50710,c_52112]) ).
cnf(c_52364,plain,
( ~ element(sK48,the_carrier(sK46))
| ~ is_a_convergence_point_of_set(sK46,sK47,sK48) ),
inference(superposition,[status(thm)],[c_52352,c_52197]) ).
cnf(c_52371,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_52364,c_52196,c_390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n001.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 21:26:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.70/1.69 % SZS status Started for theBenchmark.p
% 7.70/1.69 % SZS status Theorem for theBenchmark.p
% 7.70/1.69
% 7.70/1.69 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.70/1.69
% 7.70/1.69 ------ iProver source info
% 7.70/1.69
% 7.70/1.69 git: date: 2023-05-31 18:12:56 +0000
% 7.70/1.69 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.70/1.69 git: non_committed_changes: false
% 7.70/1.69 git: last_make_outside_of_git: false
% 7.70/1.69
% 7.70/1.69 ------ Parsing...
% 7.70/1.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.70/1.69
% 7.70/1.69 ------ Preprocessing... sup_sim: 0 sf_s rm: 11 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 0 sf_s rm: 18 0s sf_e pe_s pe_e
% 7.70/1.69
% 7.70/1.69 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.70/1.69
% 7.70/1.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.70/1.69 ------ Proving...
% 7.70/1.69 ------ Problem Properties
% 7.70/1.69
% 7.70/1.69
% 7.70/1.69 clauses 258
% 7.70/1.69 conjectures 9
% 7.70/1.69 EPR 63
% 7.70/1.69 Horn 196
% 7.70/1.69 unary 131
% 7.70/1.69 binary 61
% 7.70/1.69 lits 584
% 7.70/1.69 lits eq 21
% 7.70/1.69 fd_pure 0
% 7.70/1.69 fd_pseudo 0
% 7.70/1.69 fd_cond 1
% 7.70/1.69 fd_pseudo_cond 9
% 7.70/1.69 AC symbols 0
% 7.70/1.69
% 7.70/1.69 ------ Schedule dynamic 5 is on
% 7.70/1.69
% 7.70/1.69 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.70/1.69
% 7.70/1.69
% 7.70/1.69 ------
% 7.70/1.69 Current options:
% 7.70/1.69 ------
% 7.70/1.69
% 7.70/1.69
% 7.70/1.69
% 7.70/1.69
% 7.70/1.69 ------ Proving...
% 7.70/1.69
% 7.70/1.69
% 7.70/1.69 % SZS status Theorem for theBenchmark.p
% 7.70/1.69
% 7.70/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.70/1.69
% 7.70/1.69
%------------------------------------------------------------------------------